Question

Bird's Eye Treehouses, Inc., a Kentucky company, has determined that a majority of its customers are located in the Pennsylvania area. It therefore is considering using a lockbox system offered by a bank located in Pittsburgh. The bank has estimated that use of the system will reduce collection time by 1.5 days. Assume 365 days a year.

Average number of payments per day 740
Average value of payment $690
Variable lockbox fee (per transaction) $ .20
Annual interest rate on money market securities 4.5%


What is the NPV of the new lockbox system?

Answer 1

Answer:

NPV is -$434,544.44

Explanation:

By using the new lockbox system there would benefits in terms of savings recorded as a result of 1.5 days reduction in collection time

savings =1.5*average number of daily payments*average value of payment

savings=1.5*740*$690

savings=$765,900

However there is additional cost for using the lockbox system which is computed thus:

cost=variable lockbox fee*average number of payments per day

average lockbox fee is $0.20 per transaction

average number of payments per day is 740

cost=$0.20*740

cost=$148

the cost is meant to be incurred daily forever,hence the actual cost of the lockbox system is PV of $148 in perpetuity.

PV(perpetuity)=cash flow/(interest rate/365 days)

in order to write  down the interest rate to a daily rate

cash flow is $148

interest rate is 4.5%

PV=$148/(0.045/365)

PV=$148/0.000123288

PV=$1,200,444.44

NPV=PV of inflows-PV of ouflow

NPV=$765,900 -$1,200,444.44

NPV=-$434,544.44

Answer 2

Answer:

-$434,544

Explanation:

The reduction in cash balances associated with implementing the system can be calculated as follows;

Average Value of collection for 1.5 days = Average daily cash receipts x Reduction in collection time

Where;

Average daily cash receipts = Average number of payments per day x Average value of payment

Average daily cash receipts = 740 x $690

Average daily cash receipts = $510,600

Reduction in collection time = 1.5

Average Value of collection for 1.5 days = $510,600 x 1.5

Average Value of collection for 1.5 days = $765,900

Lockbox fee per day = Average number of payments per day x Variable lockbox fee (per transaction)

where;

Variable lockbox fee (per transaction) = $0.20

Lockbox fee per day = 740 x $0.20

Lockbox fee per day = $148

Annual Interest Rate = 4.5% = 0.045

Since all the values are on a day basis, so let us find the value on interest per day, as follows;

Daily Interest Rate = Annual Interest Rate / No. of days in a year

Daily Interest Rate = 0.045 / 365

Daily Interest Rate = 0.0001232877

Hence, Present Value of the Lock Box can be calculated as follows;

Present Value of Lock Box = Lockbox fee per day / Daily Interest Rate

Present Value of Lock Box = $148 / 0.0001232877

Present Value of Lock Box = $1,200,444

Therefore the NPV of the Lock Box can be calculated as follows;

NPV of the Lock Box = Average Value of collection for 1.5 days - Present Value of Lock Box

NPV of the Lock Box = $765,900 - $1,200,444

NPV of the Lock Box = -$434,544

Since the value of NPV is negative, Bird's Eye Treehouses, Inc., should not consider using the lock box system offered by bank in Pittsburgh.